Question

A concave mirror has a focal length of $20\text{cm}$. The distance between the two positions of the object for which the image size is double the object size is :

• A. $20\text{cm}$
• B. $40\text{cm}$
• C. $30\text{cm}$
• D. $60\text{cm}$

Answer 1

The correct option is A $20\text{cm}$

For real image in concave mirror,

$u=-u_1;v=-2u_1;f=-20\text{cm}$
($\because m=-2$ for real image)

Substituting above values in mirror formula , $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

we get, $\frac{1}{-2u_1}-\frac{1}{u_1}=-\frac{1}{20}$

$\Rightarrow u_1=30\text{cm}$

For virtual image in concave mirror:
$u=-u_2;v=2u_2;f=-20\text{cm}$
($\because m=2$ for virtual image)

Using the given data in mirror formula, we get

$\frac{1}{2u_2}-\frac{1}{u_2}=-\frac{1}{20}\Rightarrow u_2=10\text{cm}$

Therefore, distance between two positions of the object is $u=(u_1-u_2)=30\text{cm}-10\text{cm}=20\text{cm}$.

Hence, option (a) is the correct answer.